Determination of the Fractal Dimensionality of Large-Scale Structure With Type Ia Supernovae by the Method of Pairwise Distances

Abstract

A pairwise distance technique developed by the authors is used to identify signs of fractal structure in sets of extragalactic supernovae (822 type Ia supernovae in the regions 300° ≤ α ≤ 360° and 0° ≤ α ≤ 60° , − 5° ≤ δ ≤ 5°). Since the region of space occupied by the objects in the sample is highly oblate, we use Mandelbrot’s codimensionality theorem. Three cosmological models are examined: a model with a euclidean metric, a “tired light” model, and the standard ΛCDM model. Estimates of a fractal dimensionality of D ≅ 2.69 are obtained for the first two models and D ≅ 2.64 for the ΛCDM model.